基于预定义时间收敛的容噪零化神经网络求解时变Sylvester方程  

Predefined-Time Convergence-Based Noise-Tolerant Zeroing Neural Networks for Solving the Time-Varying Sylvester Equation

作　　者：岳远达 宓玲 陈川 YUE Yuanda;MI Ling;CHEN Chuan(Faculty of Mathematics and Artificial Intelligence,Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China;Key Laboratory of Computing Internet and Information Security of Ministry of Education,Shandong Computing Center(National Supercomputing Center in Jinan),Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China;Shandong Key Laboratory of Computer Network,Shandong Basic Science Research Center(Computer Science),Jinan 250014,China)

机构地区：[1]齐鲁工业大学(山东省科学院)数学与人工智能学部,山东济南250353 [2]齐鲁工业大学(山东省科学院),山东省计算中心(国家超级计算济南中心),算力互联网与信息安全教育部重点实验室,山东济南250353 [3]山东省计算机网络重点实验室,山东省基础科学研究中心(计算机科学),山东济南250014

出　　处：《聊城大学学报（自然科学版）》2024年第4期33-42,共10页Journal of Liaocheng University:Natural Science Edition

基　　金：国家重点研发计划课题(2023YFB3107303);山东省自然科学基金项目(ZR2021MF090);山东省科技型中小企业创新能力提升工程项目(2023TSGC0197)资助。

摘　　要：Sylvester方程在数学和控制理论中经常使用,而零化神经网络(ZNN)在求解此类时变方程方面非常有效。对ZNN的收敛性能进行了研究,基于一个预定义时间稳定性定理设计了一个新的激活函数,进而得到了一个用于求解时变Sylvester方程的新的ZNN模型。该模型被称为预定义时间收敛零化神经网络(PTZNN)模型。与之前的ZNN模型相比,所提出的模型提高了收敛速度使其达到了预定义时间收敛并进一步提高了容噪声能力。最后通过仿真模拟验证了该模型在求解时变Sylvester方程方面优于其他已知模型。Sylvester equations are often used in mathematics and control theory,and zeroing neural networks(ZNN)are very effective at solving such time-varying equations.The convergence of ZNN is studied,and a new activation function is designed based on a predefined time stability theorem,and a new ZNN model for solving time-varying Sylvester equations is obtained.This model is called a predefined Time Convergent zeroized neural network(PTZNN)model.Compared with the previous ZNN model,the proposed model improves the convergence speed to reach the predefined time convergence and further improves the noise tolerance.Then the simulation results show that the model is better than the known model in solving the time-varying Sylvester equation.

关 键 词：零化神经网络 容噪声能力 预定义时间收敛 SYLVESTER方程 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]